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Conference Papers Year : 2012

Entry times in automata with simple defect dynamics

Mathieu Sablik

Abstract

In this paper, we consider a simple cellular automaton with two particles of different speeds that annihilate on contact. Following a previous work by Kurka et al., we study the asymptotic distribution, starting from a random configuration, of the waiting time before a particle crosses the central column after time n. Drawing a parallel between the behaviour of this automata on a random initial configuration and a certain random walk, we approximate this walk using a Brownian motion, and we obtain explicit results for a wide class of initial measures and other automata with similar dynamics.

Dates and versions

hal-01299964 , version 1 (08-04-2016)

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Mathieu Sablik, Benjamin Hellouin de Menibus. Entry times in automata with simple defect dynamics. Automata 2012, Sep 2012, Corse, France. pp.133-141. ⟨hal-01299964⟩
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